When should you plug gear into your amplifier's effects loop and not into the standard input?
It is useful because it allows you to add effects to your sound after it has been through the amps EQ and pre-amp; What this means; the pre-amp can do its magic on a clean signal from your guitar; before effects are added.
Adding effects which boost(overdrive/distortion) the signal into the effects loop can be dangerous for the amp, as the signal has already been boosted by the pre-amp; it should be ok if you experiment with it and are careful, but is not advisable. Generally these things(boosters) should go in front of your amp; though if your preamp is up high; they will have little effect.
Modulators like phasers/chorus/delay can go in the effects loop; and will probably be better for your tone if there, since the your applying the effect to the already boosted signal from the preamp, instead of boosting a signal with an effect on it.
Unless you specifically want your modulators before the boosters this is a good rule of thumb: boosters -> preamp -> modulators.
Use the fx loop to insert delays and reverbs as the loop is after the preamp circuit. I've tried delays and verbs straight into the front of the amp and the sound can get messy when distortion is used as each repeat generated by the delay gets distorted (by the distortion). I would always put delays/verbs after distortion either using fx loop or a chain of stomp boxes. If you play clean all the time and don't use distortion then you insert the delays or verbs straight in the front of the amp. Reading previous posts the use of modulation and where to place it is upto your taste and place where it sounds and feels good to you.
In addition to @DRL's good answer, another use for the effect loop on an amp is to provide access to the power-amp in, avoiding the tone-messing-up circuitry, when you're using some modeling effects. For instance:
I have a Pod X3, which was Line6's bad-boy floor unit until recently. A modeler simulates the chain of effects, preamp, amp, cabinet, speakers, and microphone capturing the speaker's sound, if you want to enable all those things. Because they've already been factored into the sound, passing the output of the modeler into a regular guitar amp's input, through its preamp and tone controls will only screw up the sound you've worked hard to generate.
A good power-amp shouldn't modify the sound at all, except maybe add a bit of power-tube saturation or distortion, but again, the modeler has taken that into account, so we want to avoid that as much as possible.
Sticking with an overly anal/purist attitude, I also want to avoid speaker and cabinet coloration of the sound.
So, for me it made sense to buy one of Line6's Flextone III combos, and plug into its power-amp-in (effects loop return). That amp does some modeling internally but I skip past it, by going into the X3, then into the power-amp, and out its speaker. I also have a direct-out feed on the X3 if I need to go to a board.
It's kind of a waste of a pre-amp in an amp, but they're cheap now, pretty loud if need be, and very neutral sounding so the modeling is not effected.
It's just another use of the loop and ability to get between the pre-amp and amp.